Question

You are hoping to buy a house in the future and recently received an inheritance of 24,000. You intend to use your inheritance as a down payment on your house.

a.  If you put your inheritance in an account that earns 9 percent interest compounded​ annually, how many years will it be before your inheritance grows to 31,000

b.  If you let your money grow for 10.25 years at 9 percent​, how much will you​ have?

c.  How long will it take your money to grow to 31,000 if you move it into an account that pays 5 percent compounded​ annually? How long will it take your money to grow to $31,000 if you move it into an account that pays 13 percent​?

d.  What does all this tell you about the relationship among interest​ rates, time, and future​ sums?

​

Answer 1

a

In 3 years

Future value	FV=	PV * (1+r)^N
Where as:
Present value	PV=	24,000
Rate of interest	r=	9.00%
Number of years	N=	3
Future value	FV=	24000 *(1+0.09)^3
	FV=	31,080.70

b

Future value	FV=	PV * (1+r)^N
Where as:
Present value	PV=	24,000
Rate of interest	r=	9.00%
Number of years	N=	10
Future value	FV=	24000 *(1+0.09)^10.25
	FV=	58,054.09

c

5.25 years

Future value	FV=	PV * (1+r)^N
Where as:
Present value	PV=	24,000
Rate of interest	r=	5.00%
Number of years	N=	5.25
Future value	FV=	24000 *(1+0.05)^5.25
	FV=	31,006.67

1.83 years at 13%

Future value	FV=	PV * (1+r)^N
Where as:
Present value	PV=	24,000
Rate of interest	r=	13.00%
Number of years	N=	1.83
Future value	FV=	24000 *(1+0.13)^1.83
	FV=	30,015.45

d

Higher the interest rate higher the future value and viceversa. Higher the time to maturity higher the future value and vice versa.